On reachable sets for a class of nonlinear systems with constraints (Q1276329)

Nonlinear, finite-dimensional, continuous-time, nonstationary control systems are considered. The basic definitions of admissible controls and sets reachable in a given time are presented. Next, the determination of the sets reachable in a given time is investigated for a special class of nonlinear control systems with control and state trajectory constraints. The fundamental properties of the reachable sets are discussed. Moreover, the behaviours of the system trajectories are also pointed out. The paper also gives a computable procedure to generate an admissible control which steers the dynamical system from a given initial state to a reachable state. It is shown that if a state can be reached along the trajectories of the linear approximation, then it can also be reached along the trajectories of the nonlinear system. The paper extends the results presented in the paper [\textit{M. E. Achhab}, \textit{F. M. Callier} and \textit{V. Wertz}, Int. J. Robust Nonlinear Control 4, No. 2, 267-288 (1994; Zbl 0801.93011)].